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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional …
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Ji-Huan He
Silkworm cocoon has a complex hierarchic structure with discontinuity. In this paper, heat transfer through the silkworm cocoon is studied using fractal theory. The fractal approach has been successfully applied to explain the fascinating phenomenon of cocoon survival under extreme temperature environment. A better understanding of heat transfer mechanisms for the cocoon could be beneficial to the design of biomimetic clothes for special applications.
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Application Of The Fractional Complex Transform To Fractional Differential Equations, Zheng-Biao Li, Ji-Huan He
Application Of The Fractional Complex Transform To Fractional Differential Equations, Zheng-Biao Li, Ji-Huan He
Ji-Huan He
The fractional complex transform is used to analytically deal with fractional differential equations. Two examples are given to elucidate the solution procedure, showing it is extremely accessible to nonmathematicians
A Short Remark On Fractional Variational Iteration Method, Ji-Huan He
A Short Remark On Fractional Variational Iteration Method, Ji-Huan He
Ji-Huan He
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed
A New Fractal Derivation, Ji-Huan He
A New Fractal Derivation, Ji-Huan He
Ji-Huan He
A new fractal derive is defined, which is very easy for engineering applications to discontinuous problems, two simple examples are given to elucidate to establish governing equations with fractal derive and how to solve such equations, respectively.